The clip, which was filmed in 2004, shows Hanks on stage at an event for his children's school and first appeared on the website The Daily Caller.
In the video, Hanks is joined by investment banker James Montgomery, who is wearing blackface, dressed in tribal wear and holding a stuffed gorilla.
Following criticism from the Congress of Racial Equality, Hanks has issued a statement to The Wrap explaining that he did not condone the incident.
"In 2004, I was blindsided when one of the parents got up on the stage in a costume that was hideously offensive then and is hideously offensive now," he said. "What is usually a night of food and drink for a good cause was, regrettably, marred by an appalling few moments."
Montgomery has also responded to the video, saying: "Each of us does and says things at one point or another in our lives we regret. The costume I wore to the 2004 Fundraiser was one such thing for me.
"While I can understand that some people may have read something other than what was intended into my wearing that costume to a costume party, as anyone who knows me would attest, that is not consistent with my beliefs, nor is it with who I am."
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